Remotely controlled tape recorders used, for example, in a telephone message recorder, are generally provided with a mechanism which switches the recorder electrically between its different modes of operation. For example, in one known tape recorder, the magnetic head is displaced directly by a solenoid while the recorder is in the record/playback mode, whereas the switching between its fast forward mode and its re-wind mode is effected by changing the rotational direction of the motor. In such a recorder, the magnetic head is continuously attracted by the solenoid. However, a solenoid which is sufficiently powerful to directly drive the magnetic head is expensive and must be large, with the result that the electric power consumption is great. Furthermore, a reversible motor which can be switched to rotate in two directions requires complicated controls and is expensive. For this reason, it is difficult to reduce the size of such tape recorders and to lower their cost.